It is human nature to want to win an argument, be the best at something, to HAVE to be right. Although, you must ask yourself before acting on this instinct, (1) What is my end goal and ideally what do I want to accomplish? (2) Is winning really worth it? In marriage, everyone tells you to choose your battle. Is getting in an argument over taking out the trash really worth it, or should you just suck it up and do it yourself? The same goes for dealing with your residents. After all, your end goal is to keep them as residents correct?
First, don’t think about why they are wrong while they are explaining their frustrations to you, but try to empathize and put yourself in their shoes. Would you be frustrated if you had no heat or running water for over 24 hours? Most likely. Regardless of the reason why something is not getting done (that really should not be a concern or problem of theirs), your residents do not need to know that your maintenance guy quit last minute and you have no one to do the work. What they need to hear is what you are going to do about it, and that you are sorry they are having to deal with this. Acknowledge them, have empathy and find a solution.
How do you handle frustrated residents that may separate you in a unique way from your competition?